Robust state estimation for Markov jump genetic regulatory networks based on passivity theory

In this article, the robust state estimation problem for Markov jump genetic regulatory networks (GRNs) based on passivity theory is investigated. Moreover, the effect of time‐varying delays is taken into account. The focus is on designing a linear state estimator to estimate the concentrations of the mRNAs and the proteins of the GRNs, such that the dynamics of the state estimation error can be stochastically stable while achieving the prescribed passivity performance. By applying the Lyapunov–Krasovskii functional method, delay‐dependent criteria are established to ensure the existence of the mode‐dependent estimator in the form of linear matrix inequalities. Based on the obtained results, the parameters of the desired estimator gains can be further calculated. Finally, a numerical example is given to illustrate the effectiveness of our proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 214–223, 2016     

Exponential state estimator design for discrete‐time neural networks with discrete and distributed time‐varying delays

In this article, the probl of state estimation for discrete‐time neural networks with mixed time‐varying delays is investigated. The mixed time delays consist of both discrete and distributed delays. An appropriate Lyapunov–Krasovskii functional put forward to reflect the mixed time‐varying delays is proposed to establish sufficient conditions for the existence of admissible state estimators. The conditions are described in the form of linear matrix inequalities (LMIs), which guarantee the estimation error to be globally exponentially stable in the presence of mixed time‐varying delays. Then, the desired estimator matrix gain can be characterized in terms of the solution to these LMIs. A numerical example is addressed to show the effectiveness of the proposed design method. © 2014 Wiley Periodicals, Inc. Complexity 20: 38–48, 2014     

A new model for gas flow in pipe networks

We introduce a new model for gas dynamics in pipe networks by asymptotic analysis. The model is derived from the isothermal Euler equations. We present the derivation of the model as well as numerical results illustrating the validity and its properties. We compare the new model with existing models from the mathematical and engineering literature. We further give numerical results on a sample network. Copyright © 2009 John Wiley & Sons, Ltd.     

Fourth-generation warfare: Jihadist networks and percolation

This paper studies the approach to the fourth-generation warfare (4GW) paradigm from the perspective of physical and mathematical disciplines, through the interdisciplinary bridge offered by the analysis of complex networks. The study is within an emerging multidisciplinary field, Sociophysics, which attempts to apply statistical mechanics and the science of complex systems to predict human social behavior. The fourth-generation warfare concept is reviewed, and the war of the Jihadist Islam against the West will be contextualized as 4GW. The paradigm of complex systems has in diverse branches of science changed how collective phenomena are processed. The jihadist networks phenomenon in particular is appropriate for study from the standpoint of complex networks. We present an empirical study of the 9/11 and 11M networks, implemented from public information, and we give a comparison of both networks from the standpoint of complex networks. Several authors have made use of the phenomenon of percolation in complex physical systems to analyse complex networks, particularly jihadist actions like 9/11. The relationship between jihadist networks and percolation is considered. The percolation concept is reviewed and related to 4GW, and the definition of memetic dimension is introduced.     

A preferential attachment model with Poisson growth for scale-free networks

We propose a scale-free network model with a tunable power-law exponent. The Poisson growth model, as we call it, is an offshoot of the celebrated model of Barabási and Albert where a network is generated iteratively from a small seed network; at each step a node is added together with a number of incident edges preferentially attached to nodes already in the network. A key feature of our model is that the number of edges added at each step is a random variable with Poisson distribution, and, unlike the Barabási–Albert model where this quantity is fixed, it can generate any network. Our model is motivated by an application in Bayesian inference implemented as Markov chain Monte Carlo to estimate a network; for this purpose, we also give a formula for the probability of a network under our model.     

Existence and characterization of product-form invariant distributions for state-dependent stochastic networks in the heavy-traffic diffusion limit

We consider state-dependent stochastic networks in the heavy-traffic diffusion limit represented by reflected jump-diffusions in the orthant ℝ₊ ⁿ with state-dependent reflection directions upon hitting boundary faces. Jumps are allowed in each coordinate by means of independent Poisson random measures with jump amplitudes depending on the state of the process immediately before each jump. For this class of reflected jump-diffusion processes sufficient conditions for the existence of a product-form stationary density and an ergodic characterization of the stationary distribution are provided. Moreover, such stationary density is characterized in terms of semi-martingale local times at the boundaries and it is shown to be continuous and bounded. A central role is played by a previously established semi-martingale local time representation of the regulator processes. F.J. Piera’s research supported in part by CONICYT, Chile, FONDECYT Project 1070797. R.R. Mazumdar’s research supported in part by NSF, USA, Grant 0087404 through Networking Research Program, and a Discovery Grant from NSERC, Canada.     

Multistability,bifurcations, and biological neural networks: A synaptic drive firing model for cerebral cortex transition in the induction of general anesthesia

This paper focuses on multistability theory for discontinuous dynamical systems having a set of multiple isolated equilibria and/or a continuum of equilibria. Multistability is the property whereby the solutions of a dynamical system can alternate between two or more mutually exclusive Lyapunov stable and convergent equilibrium states under asymptotically slowly changing inputs or system parameters. In this paper, we extend the definition and theory of multistability to discontinuous autonomous dynamical systems. In particular, nontangency Lyapunov-based tests for multistability of discontinuous systems with Filippov and Carathéodory solutions are established. The results are then applied to excitatory and inhibitory biological neuronal networks to explain the underlying mechanism of action for anesthesia and consciousness from a multistable dynamical system perspective, thereby providing a theoretical foundation for general anesthesia using the network properties of the brain.     

A class of hierarchical queueing networks and their analysis

Queueing networks are an adequate model type for the analysis of complex system behavior. Most of the more realistic models are rather complex and do not fall into the easy solvable class of product form networks. Those models have to be analyzed by numerical solution of the underlying Markov chain and/or approximation techniques including simulation. In this paper a class of hierarchically structured queueing networks is considered and it is shown that the hierarchical model structure is directly reflected in the state space and the generator matrix of the underlying Markov chain. Iterative solution techniques for stationary and transient analysis can be modified to make use of the model structure and allow an efficient numerical analysis of large, up to now not solvable queueing networks.     

A biobjective optimization model for routing in mobile ad hoc networks

In this paper, the problem of finding optimal paths in mobile ad hoc networks is addressed. More specifically, a novel bicriteria optimization model, which allows the energy consumption and the link stability of mobile nodes to be taken into account simultaneously, is presented. In order to evaluate the validity of the proposed model, a greedy approach is devised. Some preliminary computational experiments have been carried out, in a simulation environment. The numerical results are very encouraging, showing the correctness of the proposed model. Indeed, the selection of a shorter route leads to a more stable route, but to a greater energy consumption. On the other hand, if longer routes are selected the route fragility is increased, but the average energy consumption is reduced.     

A state space model for rub‐off triangles

In this paper we suggest a distribution‐free state space model to be used with the Kalman filter in run‐off triangles. It works with original incremental amounts and relates the triangle with a column of observed values, which can be chosen in order to describe better the risk volume in each year. On the traditional application of run‐off triangles (the paid claims run‐off), this model relates the amount paid j years after the accident year with a column of observed values, that can be the claims paid on the first year, the number of claims, premiums, number of risks, etc. Two advantages of this model are the perfect split between observed values and random variables and the capacity to incorporate the changes in the speed of the company's reality into the model and in its projections. Particular care is taken on the evaluation of the final forecast mean square error as well as on the estimation of the model parameters, specially the error variances. Also, two sets of claims data are analysed. In comparison with other methods, namely, the chain ladder, the analysis of variance, the Hoerl curves and the state space modelling with the chain ladder linear model, the proposed model gave a final reserve with a mean square error within the smallest. Copyright © 2003 John Wiley & Sons, Ltd.     

Observability analysis and model formulation for nonlinear state estimation

A suitable design of state estimators for advanced control requires a detailed and representative mathematical model for capturing the nonlinear process behavior. The system observability, i.e. when the set of measurements provides enough information to estimate all the system states, is not a premise of the derivation of the Kalman filter. However, this propriety can improve the state estimator performance. On the basis of these design tasks, we outline a state estimation tuning strategy for different model formulations and present an algorithm to select the smallest number of measured variables to guarantee the system observability. The Williams–Otto semi-batch reactor was selected as case study, since its model formulation can be represented by two different set of states: (a) a mass basis states set and (b) a mass fraction basis states set. While the process-noise covariance matrix Q in the state estimator can be a diagonal and constant for the first model formulation, the matrix Q is not diagonal and time-varying for the second one due to their highly correlated states. Our results have shown how to convert the tuning matrices between different state definitions so that similar estimation results can be achieved.     

Dissipativity theory for discontinuous dynamical systems: Basic input, state, and output properties, and finite-time stability of feedback interconnections

In this paper, we develop dissipativity theory for discontinuous dynamical systems. Specifically, using set-valued supply rate maps and set-valued connective supply rate maps consisting of locally Lebesgue integrable supply rates and connective supply rates, respectively, and set-valued storage maps consisting of piecewise continuous storage functions, dissipativity properties for discontinuous dynamical systems are presented. Furthermore, extended Kalman–Yakubovich–Popov set-valued conditions, in terms of the discontinuous system dynamics, characterizing dissipativity via generalized Clarke gradients and locally Lipschitz continuous storage functions are derived. Finally, these results are used to develop feedback interconnection stability results for discontinuous dynamical systems by appropriately combining the set-valued storage maps for the forward and feedback systems.     

Approximate solution for two stage open networks with Markov-modulated queues minimizing the state space explosion problem

Analytical solutions for two-dimensional Markov processes suffer from the state space explosion problem. Two stage tandem networks are effectively used for analytical modelling of various communication and computer systems which have tandem system behaviour. Performance evaluation of tandem systems with feedbacks can be handled with these models. However, because of the numerical difficulties caused by large state spaces, considering server failures and repairs at the second stage employing multiple servers has not been possible. The solution proposed in this paper is approximate with a high degree of accuracy. Using this approach, two stage open networks with multiple servers, break downs, and repairs at the second stage as well as feedback can be modelled as three-dimensional Markov processes and solved for performability measures. Results show that, unlike other approaches such as spectral expansion, the steady state solution is possible regardless of the number of servers employed.     

Bayesian networks with a logistic regression model for the conditional probabilities

Logistic regression techniques can be used to restrict the conditional probabilities of a Bayesian network for discrete variables. More specifically, each variable of the network can be modeled through a logistic regression model, in which the parents of the variable define the covariates. When all main effects and interactions between the parent variables are incorporated as covariates, the conditional probabilities are estimated without restrictions, as in a traditional Bayesian network. By incorporating interaction terms up to a specific order only, the number of parameters can be drastically reduced. Furthermore, ordered logistic regression can be used when the categories of a variable are ordered, resulting in even more parsimonious models. Parameters are estimated by a modified junction tree algorithm. The approach is illustrated with the Alarm network.     

Effective bandwidths: Call admission,traffic policing and filtering for ATM networks

In this paper we review and extend the effective bandwidth results of Kelly [28], and Kesidis, Walrand and Chang [29, 6]. These results provide a framework for call admission schemes which are sensitive to constraints on the mean delay or the tail distribution of the workload in buffered queues. We present results which are valid for a wide variety of traffic streams and discuss their applicability for traffic management in ATM networks. We discuss the impact of traffic policing schemes, such as thresholding and filtering, on the effective bandwidth of sources. Finally we discuss effective bandwidth results for Brownian traffic models for which explicit results reveal the interaction arising in finite buffers.     

A self-organizing state space model and simplex initial distribution search

This paper proposes a method to seek initial distributions of parameters for a self-organizing state space model proposed by Kitagawa (J Am Stat Assoc 93:1203–1215, 1998). Our method is based on the simplex Nelder–Mead algorithm for solving nonlinear and discontinuous optimization problems. We show the effectiveness of our method by applying it to a linear Gaussian model, a linear non-Gaussian model, a nonlinear Gaussian model, and a stochastic volatility model.     

A probabilistic quality of service constraint for a location model of switches in ATM communications networks

We formulate a model for the optimal location of switches in ATM communications networks. The networks are designed in such a way that, at their arrival to the switches, ATM cells find free space in a buffer of length b, with a probability α. The model avoids the impairment to the communication caused by both cell loss (because of shorter buffers) and cell-delay variations (because of longer buffers). It is also shown how to transform a non-linear, probabilistic, constraint into a linear form. Computational experience is provided for the model. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Simple proof for the stability of global FIFO queueing networks

We study the stability of multiclass queueing networks under the global FIFO （first in first out） service discipline, which was established by Bramson in 2001. For these networks, the service priority of a customer is determined by his entrance time. Using fluid models, we describe the entrance time of the most senior customer in the networks at time t, which is the key to simplify the proof for the stability of the global FIFO queueing networks.